Danny Rohl’s side took advantage of Hearts’ shock 1-0 loss at St Mirren on Tuesday and the postponement of Celtic’s match at Aberdeen on Wednesday to move into second place.
Rangers are now just three points behind Hearts after their second half goal spree at Ibrox.
Rangers captain James Tavernier scored from the penalty spot in the fifth minute after Killie defender Dom Thompson was sent off for denying Djeidi Gassama a goalscoring opportunity.
Bojan Miovski drove home Rangers’ second in the 59th minute and new signing Andreas Skov Olsen scored his first goal for the club in the 74th minute after coming off the bench.
Rangers keeper Jack Butland made a mistake in the 84th minute, allowing Greg Kiltie to score a consolation goal for Kilmarnock.
But Oliver Antman and Mikey Moore scored late goals to put a gloss on the scoreline.
Hearts are due to visit Ibrox in Rangers’ next home league game.
Elsewhere on Wednesday, Marvin Bartley’s debut as Livingston boss ended in a 2-1 defeat at home to Falkirk.
Bartley took over from David Martindale on Sunday, with the former manager becoming the club’s sporting director after a 24-game winless run.
First-half goals from Kyrell Wilson and Louie Marsh proved enough for Falkirk to ruin Bartley’s first game despite Connor McLennan’s 47th-minute reply for the hosts.
Hibernian beat Dundee United 3-2 thanks to debutant Ante Suto’s stoppage-time header at Easter Road. (AFP)
